The Lightning, who have clinched the Presidents' Trophy and home-ice advantage throughout the Stanley Cup Playoffs, are 7-1-0 in their past eight games and would join the 1977-78 Montreal Canadiens (59 wins), 1976-77 Canadiens (60) and 1995-96 Detroit Red Wings (62).
Boston, which has clinched a berth into the playoffs, leads the Toronto Maple Leafs by seven points for second place in the Atlantic Division. The Maple Leafs play the Florida Panthers at Scotiabank Arena on Monday.
The Bruins have won four straight and are 17-3-1 in their past 21 games.